To belong to a family is to be woven into a collective story, like it or not. But who gets to decide when that story goes public?

Usually, of course, it’s the writer in the family, a fact underscored by the torrent of tell-all memoirs in the past decade or so. As we readers sift through the spilled beans, it’s impossible not to speculate about the behind-the-scenes battles that must often precede or follow publication. Blood relations, indeed.

From that clash of agendas — keep it private vs. tell the world — playwright Jon Robin Baitz has fashioned “Other Desert Cities,’’ now receiving its New England premiere in a first-rate SpeakEasy Stage Company production, directed with fluid assurance by Scott Edmiston.

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When “Other Desert Cities’’ begins, it’s the morning before Christmas 2004. The Iraq war is raging, and New York writer Brooke Wyeth (Anne Gottlieb) is uneasily ensconced at the Palm Springs, Calif., home of her conservative parents, Polly (Karen MacDonald) and Lyman (Munson Hicks). Also on hand are Brooke’s younger brother, a TV producer named Trip (Christopher M. Smith, excellent), and Polly’s alcoholic loose cannon of a sister, Silda (Nancy E. Carroll).

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They are arrayed around a living room, designed by Janie E. Howland, that — with its minibar, translucent chairs, and artificial silver Christmas tree — seems stuck in a mid-1960s time warp. What transpires in that living room has some of the flavor of ’60s-era generational and cultural warfare, as Baitz skillfully fuses family history and national history.

Polly and Lyman are power players in the Republican establishment whose standing is so secure that they have counted “Ron and Nancy’’ among their close friends. But Brooke has some news for them that poses a mortal threat to that standing. She’s about to publish a memoir that focuses on the missing member in the Wyeth family portrait: her beloved older brother Henry, an antiwar radical who vanished decades earlier, leaving a suicide note, after being implicated in the bombing of an Army recruiting station.

There are no photos of Henry anywhere in the Wyeth home. His disappearance from Brooke’s life permanently unsettled her; she has only recently emerged from a bout with depression for which she had to be hospitalized. She believes her parents turned their backs on Henry and are fundamentally responsible for his fate — and she says so in her book.

After sketching this scenario, a lesser playwright than Baitz might be content to assign white hats and black hats, score a few obvious points, and send the audience home aglow with self-satisfaction, all of its preexisting assumptions unchallenged. But this is neither Fox News nor MSNBC. Baitz is after deeper truths in “Other Desert Cities.’’ He wants to trace the complex strands of human motivation, compared to which party lines are a rank absurdity. At few if any points does Baitz settle for the formulaic wallow of your typical dysfunctional-family drama.

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Under producing artistic director Paul Daigneault, SpeakEasy has been on a remarkable roll lately. He contacted Baitz about staging “Other Desert Cities’’ even before its 2011 off-Broadway production, whose success took the play to Broadway. Edmiston, meanwhile, has been at the helm for superb SpeakEasy productions of plays as dissimilar as Geoffrey Nauffts’s “Next Fall,’’ Sarah Ruhl’s “In the Next Room (or the Vibrator Play),’’ and Craig Lucas’s “Reckless.’’ In matters of pace, tone, and overall shape, Edmiston seldom puts a foot wrong, whatever the subject matter.

His production of “Other Desert Cities’’ reflects an understanding that while there are five compelling figures onstage, the play pivots upon the contest of wills between daughter and mother. In dramatizing the push-pull dynamic of love and rebellion, loyalty and deep anger that informs the relationship between Brooke and Polly, Edmiston draws on the talents of two actresses who are exceptionally skilled at character portraiture.

MacDonald delivers a magnificent performance as the louder-than-life Polly, who in the first act alone wears three iridescent outfits, designed by Charles Schoonmaker. This matriarch’s weapon of mass destruction is her gift for pointed pronouncements. “Families get terrorized by their weakest member,’’ she says at one point, and it’s clear that terrorizing Polly would be no easy task. But there are multiple layers beneath her forbidding surface, and MacDonald lets us see them all. In due time.

Gottlieb’s Brooke is brimming over with competing needs: the all-consuming desire to tell Henry’s story and finally make sense of her own life, precariously balanced against the fear that publishing the memoir will sever her relationship with the parents whose approval she still, on some level, needs. To that complicated mixture of emotions Gottlieb adds a touch of steely determination — and that’s where the suspense comes in. Will she publish the book or not?

You’ll have to see “Other Desert Cities’’ to find out, and I’d strongly suggest that you do. You’re not likely to experience a more riveting drama this season.